Physics 444,  Homework, Nuclear Models:
In order to do this homework you will need to log on to the National Nuclear Data Center (NNDC). This can be accessed through the National Nuclear Data Center web page.


Once you are on the home page of the NNDC site, click on "Nuclear Structure and Decay Databases" and then select ENSDF.  You should find yourself on the page below.

http://www.nndc.bnl.gov/ensdf/

Example:
You can select data on a particular isotope, for example 17O by entering 17O in the quick search box. Then check off the first box labelled "ADOPTED LEVELS, GAMMAS". On the bottom of the page click on the HTML button as below.

Get selected ENSDF datasets:

html

At the top of the page there may be various graphical displays for the level schemes: JPEG PDF PS.  You can select one of these to see the level scheme.
If you scroll down the page you will also see text data giving you the energies of the states, the spin and parity, the life time of the state, references, the isospin T=(N-Z)/2, and the magnetic moment in nuclear magnetons. From the table or the graphical level schemes you can see that the ground state spin of 5/2+ is consistent with the shell model predictions. The first excited state is 1/2+, which is also consistent with the shell model expectations. The 2nd excited state is 1/2-, which no longer follows the simple shell model scheme so the nucleons have rearranged themselves in a different fashion. There should be a large component in the wave function for the 1/2- state of a neutron moving up to the d5/2 level where it couples with another neutron to produce a combined spin 0. This leaves a hole in the 1p1/2 state which would give the right spin and parity for the state.

  0.0
5/2+
stable
ABCD F  IJ
KLM OPQRST
UV
T=1/2; µ=-1.89379 9 (1989Ra17)
  870.7310
1/2+
179.2 ps 18
A CD F  IJ
KLM OPQR T
UV
 3055.3616
1/2-
0.08 ps +6-4
A CD F  I
KL  OPQR T
 V
 3842.84
5/2-
≤18 fs
  CD FG I
KLM  PQRST
 V

2) Shell Model
Check the following nuclei  3He, 3H,15O, 41Ca,43Ca,45Ca,47Ca,49Ca,51Ca,  67As, 69As, 71As.
Make a table for them listing the spin-parity combination, the magnetic moment in nuclear magnetons, and the quadrupole moment in barns.

a) Does the shell model give the expected spin-parities for these nuclei?
b) What is the orbital angular momentum for the Ca and As isotopes?
c) Does the magnetic moment for the Ca and As isotopes follow the expected trend predicted by the shell model? Give the evidence from the data to support your conclusion.

3) Collective Models

i) Vibrational nuclei
a) Make a table for the following nuclei:

 200Hg
 198Hg
 140Nd
 92Zr
 88Zr
spin-parity g.s.
                   
                
                   
                        
                    
spin-parity, energy 1st excited state, E1




spin-parity, energy 2nd excited state, E2




spin-parity, energy 3rd excited state, E3




spin-parity, energy 4th excited state, E4




Eavg = (E2 + E3 + E4 )/3




ratio = Eavg / E1





b) Describe qualitatively and quantitatively if the ratios in the above table are consistent with what one expects from the vibrational model. Support your conclusions.

ii) Rotational nuclei
Search on 238 Pu and at the top of the page there may be various graphic styles for the Band drawings, Select Bands:.

Using the diagram on the left for spins 0+, 2+, ...,26+ do the following:
a) Make a good quality plot of energy of the excited state on the y axis vs J(J+1) on the x axis.
b) Make the best linear fit of an equation of the form  y= a + bx ,  and determine the moment of inertia of  238 Pu.
c) Can you make a better fit going to second order? That is try y = a + bx + cx2 .
d) From these data do you conclude that 238 Pu is a rigid rotor over this span of angular momenta?